So far we have been discussing how to address the random walk with n-ary relations. Here, we consider how to integrate the temporal relations introduced in [1]} into the random walk, e.g., BEFORE, EQUAL, MEETS and etc. Instead of treating temporal relations as a separate operation from conjunction \(\wedge \) . we consider them as composite conjunction of the following form
\(P({\mathbf {x}}_h, {\mathbf {x}}_t, {\mathbf {t}}) \;\texttt {BIN}\; P^{\prime }({\mathbf {x}}_h^{\prime }, {\mathbf {x}}_t^{\prime }, {\mathbf {t}}^{\prime }) =\Big (P\left( {\mathbf {x}}_h, {\mathbf {x}}_t \right) \wedge P^{\prime }\left( {\mathbf {x}}_h^{\prime }, {\mathbf {x}}_t^{\prime } \right)\Big ) \wedge \Big (\texttt {BIN}\left( {\mathbf {t}}, {\mathbf {t}}^{\prime } \right)\Big ),\) 
